@article{meot,
title={{The ray-tracing code Zgoubi}},
journal={NIM},
volume={A 427},
pages={353-356},
author={F. M\'eot},
publisher={ },
note={This code is a plain integrator for rings without special enforcement of symplecticity.},
year={1999}}

@techreport{yokoyas,
author={Kaoru Yokoya},
title={{The Action-Angle Variables of Classical Spin Motion in Circular Accelerators}},
institution={DESY},
number={DESY 86-057},
note={},
month={June},
year={1986}}

@article{skrinskimadey,
title={{Madey's gain-spread theorem for the free-electron laser and the theory of stochastic processes}},
journal={J. Appl. Phys.},
volume={53},
pages={5453-5458},
author={S. Krinsky and J. M. Wang and P. Luchini},
publisher={},
note={},
year={1982}}

@article{skrinski,
title={{Action-angle variables and fluctuation-dissipation relations for a driven quantum oscillator}},
journal={ Phys. Rev. A},
volume={31},
pages={1267-1272},
author={Samuel Krinsky},
publisher={},
note={},
year={1985}}

@techreport{slimb,
author={D.P. Barber and H. Mais and G. Ripken},
title={{Conversion of the thin lens 8x8 formalism of the spin orbit coupling (SLIM) to a formalism usig dispersion}},
institution={DESY},
number={M-84-17},
note={},
month={May},
year={1984}}


@misc{secretb,
author={D. P. Barber},
note={Geheimer Artikel}
}

@techreport{meotaiba,
author={M. Aiba and F. M\'eot},
title={{Determination of KEK 150 MeV FFAG parameters from ray-tracing in TOSCA field maps}},
institution={CEA/CERN},
number={CEA DAPNIA-04-188 and CERN-NUFACT-Note-140},
note={},
month={May},
year={2006}}

@techreport{mane,
author={S. Mane},
title={{PTC SPIN: benchmark tests for analytically solvable models}},
institution={KEK},
number={KEK Report 2009-8},
note={},
month={September},
year={2009}}

@techreport{forestfk,
author={E. Forest},
title={{The Averaged Fokker-Planck Equation, Ergodic Averages over Invariant Tori and Synchrotron Integrals}},
institution={KEK},
number={KEK Preprint 2007-80 },
note={},
month={February},
year={2008}}


@techreport{forestfk2,
author={E. Forest},
title={{The Averaged Fokker-Planck Equation and Quantum Lifetime}},
institution={KEK},
number={KEK Preprint 2010-36 },
note={},
month={October},
year={2010}}

@techreport{seimiya,
author={D. Zhou and K. Ohmi and Y. Seimiya and Y. Ohnishi and A. Morita},
title={{SIMULATIONS ON BEAM-BEAM EFFECT UNDER
THE PRESENCE OF GENERAL CHROMATICITY}},
institution={KEK},
number={KEK Preprint 2009-10 },
note={},
month={May},
year={2009}}

@article{rajpol,
title={{Polynomial Map Factorization of Symplectic Maps}},
journal={International Journal of Modern Physics C },
volume={14},
pages={847},
author={G.  Rangarajan},
publisher={ World Scientic Publishing Company},
year={2003}}

@article{mcquisbit,
title={{Explicit geometric integration of polynomial vector fields}},
journal={BIT Numerical Mathematics },
volume={44},
pages={515-538},
author={R.I. McLachlan  and G.R.W. Quispel},
publisher={ World Scientic Publishing Company},
note={},
year={2004}}

@article{robfor,
title={{Maps for distributions and their time evolution}	},
journal={Phys. Rev. E },
volume={60},
pages={4793},
author={E. Forest and D. S. Robin},
year={1999}}

@article{wuint,
title={{Explicit Symplectic Integrator for s-dependent static magnetic field}	},
journal={Phys. Rev. E },
volume={68},
pages={},
author={Y. K. Yu and E. Forest and D. S. Robin},
year={2003}}

@article{displat,
title={{Dispersive lattice functions in a six-dimensional pseudo-harmonic-oscillator}},
journal={Phys. Rev.  },
volume={58},
pages={2481},
author={Etienne Forest},
year={1998}}

@article{tengedwards,
title={{Parameterization of Linear Coupled Motion in Periodic Systems}},
journal={IEEE Transactions on Nuclear Studies },
volume={NS-20,No.3},
pages={},
author={D. Edwards and L. Teng},
year={1973}}

@article{candy,
title={{A Symplectic Integration Algorithm for Separable Hamiltonian Functions}},
journal={J. Comput. Phys. },
volume={92},
pages={230},
author={J. Candy  and W. Rozmus},
year={1991}}

@article{locally,
title={},
journal={Phys. Rev.  },
volume={55},
pages={4665},
author={Etienne Forest},
year={1997}}

@article{chaores,
title={},
journal={Phys. Rev. Spec. Topics },
volume={6},
pages={094001},
author={Alexander W. Chao},
year={1997}}

@preprint{vivaldirot,
title={{The arithmetic of discretized rotations}},
author={F. Vivaldi},
note={Preprint},
year={2006}}

@article{morita,
title={},
journal={Phys. Rev. ST AB },
volume={6},
pages={014001},
author={A. Morita and Y. Iwashita},
year={2003}}

@article{vivaldimap,
title={{Arithmetical Method to Detect Integrability in Maps}},
journal={Phys. Rev. Lett. },
volume={90},
number={3},
author={F. Vivaldi and J.A. Roberts},
year={2003}}

@article{hiratacrossing,
title={{Analysis of beam-beam interactions with a large crossing angle}},
journal={Phys. Rev. Lett.  },
volume={74},
pages={2228-2231},
author={K. Hirata},
year={1995}}

@article{hiratamosh,
title={{A symplectic beam-beam interaction with energy change}},
journal={ KEK preprint 92-117 A and Part. Accel.},
volume={40},
pages={205-228},
author={K. Hirata and H. Moshammer and F. Ruggiero},
year={1993}}

@article{mcneuf,
title={{Composition methods in the presence of small parameters}},
journal={BIT},
volume={35(2)},
pages={258-268},
author={R. I. McLachlan},
year={1995}}

@article{langevin,
title={{Sur la th\'eorie du mouvement brownien}},
journal={Comptes-Rendus de l'Acad\'emie des Sciences},
volume={146},
pages={530-5328},
author={P. Langevin},
year={1908}}

@article{einsteinb,
title={{\"Uber die von der molekularkinetischen Theorie der W\"arme geforderte Bewegung von in ruhenden Fl\"ussigkeiten suspendierten Teilchen}},
journal={Annalen der Physik },
volume={17},
pages={549–560},
author={A. Einstein},
year={1905}}

@article{itol,
title={{On stochastic differential equations}},
journal={Mem. Amer. Math. Soc. },
volume={4},
pages={1-51},
author={K. Ito},
year={1951}}

@misc{fibreidea,
note={Unpublished idea by Machida and Mori.}
}

@misc{papaj,
note={高エネルギー加速器研究機構の西川パトリック氏との議論}
}

@misc{papa,
note={高エネルギー加速器研究機構のフォレ・エティエンヌ氏との議論}
}

@misc{adxf2,
author={R. Talman and N. Malitsky},
note={The Accelerator Description Exchange Format version 2.0 is part of the Unified Accelerator Libraries. There is a lot of documentation on the Internet including a set of lectures.  }
}

@misc{bergpoin,
author={J.S. Berg},
note={Private communication. }
}

@phdthesis{dragulescu,
author={A. Dragulescu},
title={Applications of Physics to Economics and Finance: Money, Income, Wealth and the Stock Market},
school={University of Maryland},
year={2002}}

@misc{crosslecture,
author={M. Cross},
note={ Lecture notes on statistical physics, Physics 127b, Caltech},
year={2006}}

@misc{ibuki,
author={伊吹和泰},
note={ 物性物理化学特論（大学院，秋学期）2011年度版、同志社大学},
year={2011}}

@book{gardbook,
author={C. W. Gardiner},
title={{Handbook of Stochastic Methods, Third Edition}} ,
publisher={Springer-Verlag},
address={Berlin, Germany},
year={2004}}

@book{strabook,
author={R. L. Stratonovich},
title={{Nonlinear Nonequilibrium Thermodynamics I, Linear and Nonlinear Fluctuation-Dissipation Theorems}} ,
publisher={Springer-Verlag},
address={Berlin, Germany},
year={1992}}

@book{thebook,
author={E. Forest},
title={{Beam Dynamics: A New Attitude and Framework}} ,
publisher={Harwood Academic Publishers},
address={Amsterdam, The Netherlands},
year={1997}}

@book{georgbook,
author={G. H. Hoffstaetter},
title={{High Energy Polarized Proton Beams-- A Modern View}} ,
publisher={Springer},
address={New York, USA},
year={2006}}

@book{sybook,
author={S. Y. Lee},
title={{Accelerator Physics}} ,
publisher={World Scientific Publishing},
address={},
year={2004}}

@book{butcherbook,
author={J. C. Butcher},
title={{Numerical Methods for Ordinary Differential Equations}} ,
publisher={Wiley},
address={Chichester, West Sussex, England},
year={2003}}

@book{dragtbook,
author={Alex J. Dragt},
title={{Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics}} ,
publisher={Unpublished: available in draft form},
address={Maryland, USA},
year={2004}}

@book{fp,
author={A. Lasota and M. Mackey},
title={{Probabilistic Properties of Deterministic Systems}} ,
publisher={Cambridge U. Press},
address={Cambridge, UK},
year={1985}}

@book{brouwer,
author={T. L. Saaty and J. Bram},
title={{Nonlinear Mathematics}} ,
publisher={McGraw-Hill},
address={New York, New York},
year={1964}}

@book{moser,
author={J. K. M{\"}oser},
title={{Stable and random motion in dynamical systems}} ,
publisher={Princeton University Press},
address={Princeton, New Jersey},
year={1973}}

@techreport{withsimon,
author={E. Forest and Simon Leemann},
title={{Fringe Effects in MAD, PART I,
Second Order Fringe in MAD-X   for the Module PTC}},
institution={KEK},
number={},
note={Unpublished work as of September 2005; available on request},
year={2002}}

@techreport{laslett1,
author={L. J. Laslett},
title={{Concerning the y-Growth Exhibited by Algebraic Transformations}	},
institution={MURA},
number={Mura Report 246},
note={It can also be found in LBNL PUB-616: Selected Works of L. Jackson Laslett, (1987).},
year={1957}}

@techreport{laslett2,
author={L. J. Laslett},
title={{Round-Off Errors From Fixed-Point Linear Algebraic Transformations Computed by {IBM-704}
Program 117}},
institution={MURA},
number={Mura Report 302},
year={1957}}

@misc{cole,
note={This is from an unpulished article of Dr.~Cole called O Camelot ! a memoir of the MURA years, 1994. It can be found on the Web or at 
the American Institute of Physics, Center for History of Physics, Niels Bohr Library. One Physics Ellipse, College Park, MD 20740, USA. 
Call Number IH 1995-0021.}
}


@techreport{bmad,
author={D. Sagan},
title={{The BMAD Reference Manual}	},
institution={Cornell},
number={Revision: 5.5},
year={2005}}

@techreport{patricia2,
author={H. Weidemann},
title={},
institution={SLAC},
number={PEP Technical Memo 230},
year={1981}}

@techreport{patricia1,
author={H. Weidemann},
title={},
institution={SLAC},
number={PEP Note 220},
year={1976}}

@techreport{furmanite,
author={M. Furman},
title={{Simple Method to Symplectify Matrices}	},
institution={SSC Central Design Group},
number={SSC-TM-4001},
year={1985}}

@techreport{schoch,
author={A. Schoch},
title={},
institution={CERN},
number={CERN 57-21},
year={1958}}

@techreport{race,
author={A. Wrulich},
title={{RACETRACK: A Computer code for the simulation of particle motion}},
number={DESY 84-026},
year={1984}}


@techreport{ptc,
author={E. Forest and F. Schmidt and E. McIntosh},
title={{Introduction to the Polymorphic Tracking Code}},
number={CERN-SL-2002-044, KEK-Report 2002-3},
institution={CERN/KEK},
year={2002}}



@techreport{forestdemoivre,
author={E. Forest},
title={{Unified View of Lattice Functions as Representations of Complex Numbers // Bonus: Chao falls out of Sands / /Bonus: Dragt’s Quadratic Kinematic Invariants fall out }},
number={KEK Preprint 2010-38},
institution={KEK},
year={2010}}

@inproceedings{fppepac,
booktitle={{Proceedings of the European Accelerator Physics Conference}} ,
title={{Map  Creation and Analysis via Overloaded Tools in Fortran 90}},
author={E. Forest and F. Schmidt},
publisher={Joint Accelerator Conferences Website},
address={Vienna, Austria},
note={},
pages={1399},
year={2000}}

@inproceedings{fppipac2006,
booktitle={{Proceedings of ICAP 2006}} ,
title={{The FPP and PTC Libraries}},
author={E. Forest and Y. Nogiwa},
publisher={Joint Accelerator Conferences Website},
address={Chamonix, France},
note={},
pages={21},
year={2006}}

@inproceedings{ptcipac2006,
booktitle={{Proceedings of ICAP 2006}} ,
title={{New Developments of MAD-X using PTC}},
author={P. K. Skowronski and F. Schmidt and R. de Maria and E. Forest},
publisher={Joint Accelerator Conferences Website},
address={Chamonix, France},
note={},
pages={209},
year={2006}}

@article{fortranforum,
author={E. Forest and F. Schmidt},
title={{The ``full polymorphic package'' (FPP)}},
journal={ACM SIGPLAN Fortran Forum  },
volume={20},
pages={12-17},
note={(N.Y., USA)},
year={2001}}

@misc{fpphtml,
note={FPP, the Fully Polymorphic Package is being documented on the WEB by E.~Forest and Y.~Nogiwa. It is completely independent of any tracking code. It can be used in any program: it simply facilitate the extraction of Taylor series and the normalization of Taylor maps. 
It is based on a version of Berz Package. }
}

@inproceedings{sardenia,
booktitle={{Proceedings of the Joint US-CERN School on Particle  Accelerators, Sardenia} } ,
title={{Nonlinear Dynamics Aspects of Particle  Accelerators}},
publisher={Springer-Verlag},
address={Berlin, Germany},
note={},
pages={},
year={1985}}

@misc{despottracyii,
note={TracyII was developed by Johan Bengtsson based on the codes Tracy and Gemini of H.~Nishimura. Despot was developed by 
E.~Forest and was essentially like TracyII except that it could perform TPSA calculations with parameter dependence in a way similar to SixTrack of F.~Schmidt.}
}

@misc{OO_Fortran90,
note={V. K. Decyk and  C. D. Norton and B. K. Szymanski, Introduction to Object-Oriented Concepts using Fortran90, to be published}}

@techreport{willeke,
author={F. Willeke},
title={},
institution={Fermilab},
number={FN-422},
year={1985}}

@article{cs,
title={},
journal={Ann. Phys.  },
volume={3},
pages={1},
author={E. D. Courant and H. S. Snyder},
note={(N.Y.)},
year={1958}}

@article{dragtmom,
title={GENERAL MOMENT INVARIANTS FOR LINEAR HAMILTONIAN SYSTEMS},
author={A. Dragt and F. Neri and G. Rangarajan},
journal={Physical Review A },
volume={45},
pages={2572},
note={(N.Y.)},
year={1992}}

@book{controltheory,
author={J. G. Truxal},
title={{Control System Synthesis}} ,
publisher={McGraw-Hill},
address={New York},
year={1955}}

@book{controltheory2,
author={Chi-Tsong Chen},
title={{ Linear System Theory and Design}} ,
publisher={Holt, Rinehart and Winston},
address={New York},
year={1984}}

@inproceedings{chaosmear,
booktitle={{Proceedings of the Second Advanced ICFA Beam Dynamics Workshop}} ,
title={},
publisher={Holt, Rinehart and Winston},
address={New York},
note={CERN 88-04},
pages={152},
year={1988}}

@inproceedings{vertical,
author={E. Forest and H. Nishimura},
booktitle={{Proceedings of the 1989 Particle Accelerator Conference}} ,
title={{Vertically Integrated Simulation Tools for
Self-Consistent Tracking and Analysis}},
publisher={},
address={},
note={Also LBL-25961},
pages={1304},
year={1989}}

@inproceedings{elleaume,
author={P. Elleaume},
booktitle={{Proceedings of the 1992 European Particle Accelerator Conference}} ,
title={{A New Approach to the Electron Beam Dynamics in Undulators and Wigglers}},
publisher={Editions Frontiers},
address={Berlin},
note={},
pages={661},
year={1992}}

@incollection{adref,
author={L. B. Rall},
title={{ Automatic Differentiation: Techniques and Application}} ,
booktitle={{Lecture Notes in Computer Science}},
publisher={ Springer-Verlag },
series={120},
year={1981}}

@inproceedings{adsiam,
booktitle={{SIAM}} ,
title={{Automatic Differentiation of Algorithms: Theory,
Implementation, and Application}},
author={},
publisher={},
address={Philadelphia, PA},
note={},
pages={},
year={1991}}

@article{bitch,
author={Z. Parsa and S. Tepikian and E. D. Courant},
title={},
journal={Part. Accel. },
volume={22},
pages={205},
note={},
year={1987}}

@phdthesis{merminga,
author={N. Merminga},
title={},
school={University of Michigan},
year={1989}}

@phdthesis{makino,
author={K. Makino },
title={{Rigourous Analysis of Nonlinear Motion in Particle Accelerators}},
school={Michigan State University},
year={1998}}

@techreport{mermingang,
author={N. Merminga and K.-Y. Ng},
title={},
institution={SSC-CDG},
number={SSC-N-594},
year={1989}}

@techreport{guignard,
author={G. Guignard},
title={{A General Treatment of Resonances in Accelerators}},
institution={CERN},
number={CERN 78-11},
year={1978}}


@inproceedings{crw,
booktitle={{Physics of High Energy Particle Accelerators}} ,
title={{ AIP Conference Proceedings} },
author={E. D. Courant and R. D. Ruth and W. T. Weng},
publisher={American Institute of Physics},
address={New York},
volume={127},
pages={294},
year={1985}}


@article{vonzeipel,
author={H. Von Zeipel},
title={},
journal={Arkiv Mat. Astron. Fys.  },
volume={31},
number={1},
pages={7},
note={},
year={1916}}

@article{ando,
author={A. Ando},
title={},
journal={Part. Accel.  },
volume={15},
number={},
pages={177},
note={},
year={1984}}

@techreport{bengtsson,
author={Johann Bengtsson},
title={},
institution={CERN},
number={CERN 88-05},
year={1988}}

@techreport{schmidtwilleke,
author={Frank Schmidt and Ferdinand Willeke},
title={},
institution={CERN},
number={CERN SPS/88-30},
year={1988}}

@article{hori,
author={G. Hori},
title={{Theory of General Perturbations with Unspecified Canonical Variables}},
journal={ Publ. Astr. Soc. Japan  },
volume={18},
number={},
pages={287},
note={},
year={1966}}

@article{nagaokahara,
author={R. Nagaoka and K. Yoshida and M. Hara},
title={{High Order Sextupoles Resonances in Low-Emittance Light Source Storage Rings}},
journal={Part. Accel.},
volume={33},
number={},
pages={57},
note={},
year={1990}}



@article{deprit,
author={A. Deprit},
title={},
journal={Cel. Mech.},
volume={1},
number={},
pages={12},
note={},
year={1969}}

@article{michelotti2',
author={Leo Michelotti},
title={},
journal={Part. Accel.},
volume={19},
number={},
pages={236},
note={},
year={1987}}

@inproceedings{adsiam,
booktitle={{ AIP Conference Proceedings }} ,
title={},
author={Leo Michelotti},
publisher={American Institute of Physics},
address={},
volume={153},
pages={236},
year={1987}}

@article{warnocktori,
author={R. L.  Warnock and R. D. Ruth},
title={},
journal={Physica D},
volume={56},
number={},
pages={188},
note={},
year={1992}}

@article{rwg,
author={W. E. Gabella and R. D. Ruth and R. L. Warnock},
title={},
journal={Phys. Rev. A},
volume={46},
number={},
pages={3493},
note={},
year={1992}}

@article{warnockmap,
author={J. S. Berg and  R. L. Warnock and R. D. Ruth and E. Forest},
title={{Construction of Symplectic Maps for Nonlinear Motion of Particles in Accelerators}},
journal={Phys. Rev. E},
volume={49},
number={},
pages={722},
month={Jan},
year={1994},
note={Also see  SLAC-PUB-6037 and 6164}}

@techreport{warconv,
author={R. L. Warnock and J.A. Ellison},
title={{Convergence of a Fourier-Spline Representation for the Full-turn Map Generator}},
institution={Stanford Linear Accelerator Center},
number={ SLAC-PUB-7465},
month={April},
year={1997},
note={Also appeared in the Proceedings of the Conference on Particle Beam Stability and Nonlinear Dynamics, Institute of 
Theoritical Physics, Santa Barbara, December 3-5, 1996, API Conference Proceedings}
}

@techreport{warcar,
author={R. L. Warnock and J. A. Ellison},
title={{From Symplectic Integrator to Poincar\'e Map: Spline Expansion of a Map Generator in Cartesian Coordinates}},
institution={Deutsches Elektronen-Synchrotron},
number={ DESY 97-163 and also SLAC-PUB-7465},
month={August},
year={1997},
note={}
}

@techreport{warbergres,
author={R. L. Warnock and J. S. Berg},
title={{Fast Symplectic Mapping and Long-term Stability Near Broad Resonances}},
institution={Stanford Linear Accelerator Center},
number={ SLAC-PUB-7464},
month={April},
year={1997},
note={Also appeared in the Proceedings of the ICFA Workshop on Nonlinear and Collective Phenomena in Beam Physics, Archidosso, Italy, September 2-6, 1996, AIP Conference Proc. 395  eds M Cornacchia and C Pelligrini}
}



@techreport{collins,
author={T. L. Collins},
title={{Distortion functions}},
institution={Fermilab},
number={ Fermilab-84/114},
month={Oct},
year={1984}
}

@inproceedings{autin,
booktitle={{ AIP Conference Proceedings }} ,
title={},
author={B. Autin},
publisher={American Institute of Physics},
address={},
volume={153},
note={},
pages={236},
year={1987}}

@article{antillon,
author={A. Antill{\`o}n},
title={},
journal={ Part. Accel.},
volume={ 23},
number={},
pages={187},
month={},
year={1988},
note={}}

@inproceedings{brownserv,
booktitle={{AIP Conference Proceedings }} ,
title={},
author={K. Brown and R. Servranckx},
publisher={American Institute of Physics},
address={},
volume={127},
note={},
pages={62},
year={1985}}

@article{berzfringeaccurate,
author={M. Berz and B. Erdelyi  and K. Makino},
title={{Towards Accurate Simulation of Fringe Field Effects}},
journal={ Nucl. Instr. and Meth.},
volume={  A472},
number={},
pages={533-540},
month={},
year={2001},
note={}}

@article{berzopt,
author={B. Erdelyi and M. Berz},
title={{Towards Accurate Simulation of Fringe Field Effects}},
journal={ Phys. Rev. Lett.},
volume={  87(11)},
number={},
pages={114302},
month={},
year={2001},
note={}}

@article{berzfringelarge,
author={M. Berz and B. Erdelyi  and K. Makino},
title={{Fringe field effects in small rings of large acceptance}},
journal={ Phys. Rev. ST-Accel. Beams},
volume={  3},
number={},
pages={124001},
month={},
year={2000},
note={}}

@article{cosy5ham,
author={M. Berz and H. C. Hoffmann and H. Wollnik},
title={},
journal={ Nucl. Instr. and Meth.},
volume={  A258},
number={},
pages={402},
month={},
year={1987},
note={}}

@techreport{cosy,
author={M. Berz},
title={{COSY INFINITY Version 8}},
journal={},
volume={  },
number={},
pages={},
institution={Michigan State University},
month={January},
year={2000},
note={}}

@techreport{irwinkick,
author={J. Irwin},
title={A MULTIKICK FACTORIZATION ALGORITHM FOR NONLINEAR MAPS},
journal={},
volume={  },
number={SSC-228},
pages={},
institution={SSC Central Design Group},
month={January},
year={1989},
note={}}

@article{abellschmidt,
author={D. T. Abell and F. Schmidt and E. McIntosh},
title={{Fast Symplectic Map Tracking for the CERN Large Hadron Collider}},
journal={ Phys. Rev. Special Topics - Accelerators and Beams},
volume={  6},
number={},
pages={},
month={},
year={2003},
note={}}


@inproceedings{brownservcode,
booktitle={{AIP Conference Proceedings}} ,
title={},
author={K. Brown and R. Servranckx},
publisher={American Institute of Physics},
address={},
volume={153},
note={},
pages={123},
year={1987}}

@inproceedings{dragtabell,
booktitle={{ }} ,
title={},
author={A. J. Dragt and D. Abell},
publisher={},
address={},
volume={},
note={Proceedings of ${\rm 15}^{\rm th}$ International Conference on  High Energy Accelerators, to appear in 1993},
pages={},
year={}}

@phdthesis{abellthesis,
booktitle={{ }} ,
title={{Analytic Properties and Cremona Approximation of Transfer Maps for Hamiltonian Systems}},
author={D. T. Abell},
publisher={University of Maryland},
address={College Park, Maryland, USA},
volume={},
note={},
pages={},
year={1995}}

@techreport{ivan,
author={I. Gjaja},
title={{Monomial Factorization of Symplectic Maps}},
institution={Dynamical Systems and Accelerator Theory Group,
Physics Department, University of Maryland },
number={ },
month={},
year={1989}}

@inproceedings{douglas,
booktitle={{ AIP Conference Proceedings}} ,
title={},
author={D. R. Douglas},
publisher={American Institute of Physics},
address={},
volume={153},
note={},
pages={390},
year={1987}}

@inproceedings{douglasetienne,
booktitle={} ,
title={A Method to Render Second Order Beam Optics Programs Symplectic},
author={D. R. Douglas and E. Forest and R. V. Servranckx},
publisher={IEEE Transaction on Nuclear Science},
address={},
volume={NS-32, No. 5},
note={},
pages={2279},
year={1985}}

@article{tpsa,
author={M. Berz},
title={The Method of Power Series Tracking for the Mathematical Description of Beam Dynamics},
journal={ Nucl. Instr. and Meth.},
volume={  A258},
number={},
pages={431},
month={},
year={1987},
note={}}

@article{berz,
author={M. Berz },
title={},
journal={Part. Accel.},
volume={ 24},
number={},
pages={109},
month={},
year={1989},
note={}}

@article{berzhoft,
author={G.H. Hoffst\"atter and M. Berz },
title={{Symplectic scaling of transfer maps including fringe fields}},
journal={Phys. Rev. E.},
volume={54},
number={5},
pages={109},
month={November},
year={1996},
note={}}

@inproceedings{berzpinv,
booktitle={{ AIP Conference Proceedings} } ,
title={},
author={M. Berz},
publisher={American Institute of Physics},
address={},
volume={184},
note={},
pages={961},
year={1989}}

@techreport{garczynski,
author={V. Garczynski},
title={},
institution={ Brookhaven National Laboratory},
number={ AD/AP-47},
month={},
year={1992}}

@inproceedings{ad,
booktitle={{ Transactions of the First Army Conference on Applied Mathematics and Computing}} ,
title={},
author={G. Corliss and L. B. Rall},
publisher={},
address={},
volume={ARO},
note={Report 84-1},
pages={},
year={1984}}

@article{fbi,
author={E. Forest and M. Berz and J. Irwin },
title={},
journal={Part. Accel.},
volume={ 24},
number={},
pages={91},
month={},
year={1989},
note={}}

@article{dragtfinn,
author={A. J. Dragt and  J. M. Finn },
title={{Lie series and invariant functions for analytic symplectic maps}},
journal={J. Math. Phys.},
volume={ 17},
number={},
pages={2215-2227},
month={},
year={1976},
note={}}

@article{forestreview,
author={E. Forest },
title={{Geometric integration for particle accelerators}},
journal={J. Phys. A: Math. Gen.},
volume={ 39 },
number={},
pages={5321-5377},
month={},
year={2006},
note={}}

@misc{marylie,
note={This is a code that parametrizes  Taylor series maps around the design orbit
using Lie operators in the Dragt-Finn factorization. Presently the most complete
version of this code has a library of third order maps. 
}}

@misc{michel1,
note={The original work of Michelotti falls in this category: the application of Lie methods
to standard accelerator theory.
}}

@misc{dalie,
note={E. Forest and J. Bengtsson have worked out a library based on automatic differentiation which allows power series
normalization, various factorizations (Dragt-Finn, Irwin) and the computation of generating functions. It also normalizes
maps in the nonsymplectic case which is useful in electron machines.}}

@misc{classic,
note={An effort, dubbed CLASSIC, is under way at SLAC, Fermilab and CERN to produce an object
oriented particle dynamics code for accelerators.}}

@misc{sad,
note={Code by K.~Oide et al., Japanese documentation can be found on KEK internet site: http://acc-physics.kek.jp/sad/ }}


@phdthesis{healy,
author={L. M. Healy},
title={{Lie Algebraic Methods for Treatting Lattice Parameter Errors in Particle Accelerators}},
school={University of Maryland},
year={1986}}

@phdthesis{ryne,
author={R. D. Ryne},
title={{Lie Algebraic Treatment of Space Charge}},
school={University of Maryland},
year={1986}}

@article{healymis,
author={L. M. Healy and A. J. Dragt and I. M. Gjaja},
title={{Computation of Error Effects in Nonlinear Hamiltonian Systems using Lie Algebraic Methods}},
journal={J. Math. Phys.},
volume={ 33},
number={6},
pages={1948},
month={June},
year={1992},
note={}}


@inproceedings{krejcik,
booktitle={{Proceedings of the IEEE PAC Conference }} ,
title={},
author={P. Krejcik},
publisher={IEEE},
address={New York},
volume={},
note={},
pages={1278},
year={1987}}

@article{halbach,
author={K. Halbach},
title={},
journal={ Nucl. Instr. and Meth.},
volume={ A187},
number={},
pages={109},
month={},
year={1981},
note={}}

@techreport{jager,
author={J. J{\"a}ger and D. M{\"o}hl},
title={},
institution={ CERN},
number={ PS/DL/LEAR/Note 81-7},
month={},
year={1981}}

@article{dragtchrom,
author={A. J. Dragt},
title={},
journal={ Part. Accel. },
volume={ 12},
number={},
pages={205},
month={},
year={1982},
note={}}

@techreport{lego,
author={E. Forest and K. Hirata},
title={{A Contemporary Guide to Beam Dynamics}},
institution={ KEK},
number={92-12},
month={August},
year={1992}}

@article{teapot,
author={L. Schachinger and R. Talman},
title={},
journal={ Part. Accel. },
volume={ 22},
number={},
pages={35},
month={},
year={1987},
note={E.~Forest  checked TEAPOT against the PSR lattice paper of Dragt for the appendix of this paper.}}



@inproceedings{machida,
booktitle={{Proceedings of the Computational Accelerator Physics  Conference }} ,
title={{The Simpsons Program: 6-D Phase Space Tracking with Acceleration}},
author={S. Machida},
publisher={American Institute of Physics},
address={New York},
volume={},
note={},
pages={},
year={1993}}

@misc{mad1,
note={What follows is a private communication from Chris Iselin of CERN.
`` The approach to rotation and displacement described in the MAD User's 
guide is also used to define the global machine geometry (in fact to tell 
where the different lego pieces sit in space).  I found the idea in the 
old TRANSPORT program, which has an option to compute ``floor coordinates''. 
It uses a 3-vector and a 3-by-3-matrix to represent the Euclidean group, 
and it applies these both to the global layout and for computing the 
effect of misaligned elements.  I just ported this mechanism to MAD.
}}

@misc{mad2,
author={C. Iselin},
title={{The MAD User's guide}},
journal={  },
volume={ },
number={},
pages={},
month={},
year={},
note={The most up-to-date version can be found at CERN and is available on the internet.}}

@misc{madnew,
author={C. Iselin and Hans Grote and Frank Schmidt and others},
title={{The MAD8, MAD9 and MAD-X programmes}},
journal={  },
volume={ },
number={},
pages={},
month={},
year={},
note={The most up-to-date version can be found at CERN and is available on the Internet. The symplectic integrator PTC of Forest, Schmidt and McIntosh is now embedded in MAD-X.}}

@article{hamfree,
author={E. Forest},
title={{A Hamiltonian-free description of single particle dynamics for hopelessly complex periodic systems}},
journal={ J. Math. Phys. },
volume={ 31},
number={},
pages={1133},
month={},
year={1990},
note={originally, SSC-111, 1987.}}

@article{hamfredo,
author={A. Bazzanni and P. Mazzanti and G. Servizi and G. Turchetti},
title={},
journal={Nuovo Cimento },
volume={ B},
number={102},
pages={51},
month={},
year={1988},
note={}}

@inproceedings{hamdragt,
booktitle={{Proceedings of the 1984 Study on the Design and Utilization of the
Superconducting Super Collider}},
title={},
author={A. J. Dragt},
editor={R. Donaldson and J. Morfin },
publisher={Am. Phys. Soc., New York},
address={Snowmass},
volume={},
note={},
pages={},
year={1985}}

@techreport{pseudopeggs,
author={S. G. Peggs},
title={},
institution={ },
number={SSC-17},
month={},
year={1988},
note={Presented at {\rm XIV} International Conference on High Energy Accelerators, Tsukuba, Japan 22-26 August 1989.
}}


@techreport{jackson,
author={A. Jackson},
title={},
institution={ },
number={SSC-107},
month={},
year={1987},
note={}}

@techreport{analsmear,
author={E. Forest},
title={},
institution={ },
number={SSC-95},
month={},
year={1986},
note={}}

@techreport{bengtssonirwin,
author={J. Bengtsson and J. Irwin},
title={},
institution={ },
number={SSC-232},
month={},
year={1990},
note={}}

@inproceedings{singleres,
booktitle={{Nonlinear Problems in Future Particle Accelerators, Capri, Italy}} ,
title={},
author={E. Forest and J. Irwin},
editor={ W. Scandale and G. Turchetti},
publisher={World Scientific},
address={Singapore},
volume={},
note={},
pages={46},
year={1990}}

@article{forestjanko,
author={E. Forest and J. Milutinovic},
title={},
journal={ Nucl. Instr. Meth. },
volume={ A269},
number={},
pages={474},
month={},
year={1988},
note={}}

@techreport{ohmi,
author={E. Forest and K. Ohmi},
title={{Symplectic Integration in Complex Wigglers }},
institution={ KEK},
number={92-14},
month={September},
year={1992}}


@article{forebenreu,
author={E. Forest and J. Bengtsson and M. Reusch},
title={{Application of the Yoshida-Ruth techniques to implicit integration and multi-map explicit integration}},
journal={ Phys. Lett. A},
volume={ 5},
number={},
pages={99},
month={},
year={1991},
note={}}

@article{liepot,
author={E. Forest},
title={},
journal={ Phys. Lett. A},
volume={ 22},
number={},
pages={15},
month={},
year={1987},
note={}}

@article{review,
author={A. J. Dragt et al.},
title={},
journal={ Ann. Rev. Nucl. Sci.},
volume={ 38},
number={},
pages={455},
month={},
year={1988},
note={}}

@article{ruthforest,
author={E. Forest and R. D. Ruth},
title={{Fourth-Order Symplectic Integration}},
journal={ Physica {\bf D}},
volume={ 43},
number={},
pages={105},
month={},
year={1990},
note={}}

@techreport{francesco,
author={K. Hirata and F. Ruggiero},
title={{Treatment of Radiation in Electron Storage Rings}},
institution={ CERN},
number={LEP Note 611},
month={},
year={1988},
note={
}}

@article{sixth,
author={E. Forest },
title={{Sixth-Order Lie Group Integrator}},
journal={ J. Comp. Phys.},
volume={ 99},
number={ 2},
pages={209},
month={},
year={1992},
note={}}


@article{ruthoriginal,
author={R.D. Ruth},
title={},
journal={ IEEE Trans. Nucl. Sci.},
volume={ Ns-30},
number={ },
pages={2669},
month={},
year={1983},
note={}}

@misc{neri,
note={Filippo Neri first realized that Ruth's algorithms were connected to Lie groups i.e. exponential operators. }}

@article{yoshida,

author={H. Yoshida},
title={{Construction of higher order symplectic integrators}},
journal={ Phys. Lett. A},
volume={ 150},
number={ },
pages={262},
month={},
year={1990},
note={}}

@article{tenged,
author={D. A. Edwards and L. C. Teng},
title={},
journal={ IEEE Trans. Nucl. Sci.},
volume={NS-20},
number={ },
pages={885},
month={},
year={1983},
note={}}

@book{arnold,
author={V. I. Arnold},
title={{Mathematical Methods of Classical Mechanics}},
publisher={Springer-Verlag},
address={New York},
year={1978}}

@article{lsmith,
author={L. Smith},
title={{Effects of Wigglers and Undulators on
Beam Dynamics}},
institution={ LBNL},
number={ESG Tech Note-24},
month={January},
year={1986},
note={
}}

@techreport{swapon,
author={S. Chattopadhyay},
title={{Some Fundamental Aspect of Fluctuations and Coherence in Charged-Particle Beams in Storage Rings}},
institution={ CERN},
number={CERN 84-11},
month={October},
year={1984},
note={
}}

@book{edwardssyphers,
author={D. A. Edwards and M. J. Syphers},
title={{An Introduction to the Physics of High Energy Accelerators}} ,
publisher={Wiley},
series={Wiley Series in Beam Physics and Accelerator Technology},
address={New York},
year={1993}}

@book{michelbook,
author={Leo Michelotti},
title={{Intermediate Classical Dynamics with Applications to Beam Physics}} ,
publisher={Wiley},
series={Wiley Series in Beam Physics and Accelerator Technology},
address={New York},
year={1995}}

@book{hamermesh,
author={M. Hamermesh},
title={{Group theory and its application to physical problems}} ,
publisher={Addison-Wesley},
series={},
address={Reading, Mass.},
year={1962}}

@book{statonovich,
author={Rouslan L. Stratonovich},
title={{Nonlinear Nonequilibrium Thermodynamics I: Linear and Nonlinear Dissipation Theorems}} ,
publisher={Springer-Veslag},
series={},
address={Berlin, FRG},
year={1992}}

@techreport{wilson,
author={E. Wilson},
title={{Transverse Beam Dynamics}},
institution={ CERN},
number={CERN 84-19},
month={November},
year={1985},
note={
}}

@inproceedings{ruthsardinia,
booktitle={{Nonlinear Dynamics Aspects of Particle Accelerators}} ,
title={{Single Particle Dynamics and Nonlinear Resonances in Circular Accelerators}},
publisher={Springer-Verlag},
address={Berlin},
author={R. D. Ruth},
note={},
editor={J. M. Jowett and M. Month},
pages={37},
year={1986}}

@inproceedings{jowettsardinia,
booktitle={{Nonlinear Dynamics Aspects of Particle Accelerators}} ,
title={{Non-linear Dissipative Phenomena in Electron Storage Rings}},
publisher={Springer-Verlag},
address={Berlin},
author={John. M. Jowett},
note={},
editor={J. M. Jowett and M. Month},
pages={343},
year={1986}}


@techreport{koseleff,
author={P.-V. Koseleff },
title={{Formal Calculus for Lie Methods in Hamiltonian Mechanics}},
institution={ LBL},
number={LBID-2030 Rev.},
month={November},
year={1994},
note={Translated by D. Boucher and E. Forest
}}

@inproceedings{alexalphac,
booktitle={{XVth International Conference on High Energy Accelerators}} ,
title={{Recent Efforts in Nonlinear Dynamics}},
author={A. W. Chao},
publisher={World Scientific},
address={Singapore},
note={},
editor={J. Rossbach},
pages={981},
year={1993}}

@inproceedings{emery,
booktitle={{XVth International Conference on High Energy Accelerators}},
title={{Coupling of Betatron Motion to the Longitudinal Plane Through Path
Lengthening in Low-$\alpha_c$ Storage Rings}},
author={L. Emery},
publisher={World Scientific},
address={Singapore},
note={},
editor={J. Rossbach},
pages={1172},
year={1993}}

@article{smallmach,
author={E. Forest and M. F. Reusch and D. Bruhwiler and A. Amiry},
title={{The Correct Local Description for Tracking In Rings}},
journal={Part. Accel. },
volume={45},
pages={66},
note={},
year={1994}}

@article{chaorad,
author={A. W. Chao},
title={},
journal={J. Appl. Phy. },
volume={50},
pages={595},
note={},
year={1979}}

@article{bogs,
author={A. W. Chao},
title={},
journal={J. Appl. Phy. },
volume={50},
pages={595},
note={},
year={1979}}

@article{chaoslim,
author={A. W. Chao},
title={},
journal={Nucl. Instr. Meth. },
volume={180},
pages={29},
note={},
year={1981}}


@article{robiniso,
author={D. Robin and  E. Forest and  C. Pellegrini and A. Amiry},
title={{Quasi-Isochronous Storage Rings}},
journal={Phys. Rev. E. },
volume={48},
pages={2149},
note={},
month={September},
year={1993}}

@article{horid,
author={G. Hori},
title={{Theory of General Perturbations for Non-Canonical Systems}},
journal={Publ. Astr. Soc. Japan},
volume={23},
number={},
pages={567},
note={},
year={1971}}

@inproceedings{dragtfermi,
booktitle={} ,
title={{ Lectures on Nonlinear Orbit Dynamics }},
author={A. J. Dragt},
publisher={American Institute of Physics},
address={New York},
volume={87},
pages={147},
year={1981}}

@article{kahn,
author={P. B. Kahn and Y. Zarmi},
title={},
journal={Physica D},
volume={54},
number={},
pages={65},
note={},
year={1991}}

@book{siegel,
author={C. L. Siegel and J. K. M{\"o}ser},
title={{Lectures on Celestial Mechanics }} ,
publisher={Springer},
address={Berlin},
year={1971}}

@article{diana,
author={E. Forest and D. Murray},
title={{Freedom in Minimal Normal Forms}},
journal={Physica D},
volume={74},
number={},
pages={181},
note={},
year={1994}}

@book{gasio,
author={S. Gasiorowicz},
title={{Quantum Physics}} ,
publisher={Wiley},
address={New York},
note={Chapter 7 contains a very readable account of operator methods in quantum mechanics},
year={1974}}

@article{peggstalman,
author={S. G. Peggs and R. M. Talman},
title={{Nonlinear Problems in Accelerator Physics}},
journal={Ann. Rev. Nucl. Part. Sci.},
volume={36},
number={},
pages={287},
note={},
year={1986}}

@article{masuosuzuki,
author={M. Suzuki},
title={{General Nonsymmetric Higher-Order Decomposition of Exponential Operators and Symplectic Integrators}},
journal={J. Phys. Soc. Jpn.},
volume={61},
number={},
pages={3015-3019},
note={},
month={},
year={1992}}

@article{bandrauk,
author={A. D. Bandrauk and H. Shen},
title={},
journal={Chem. Phys. Lett.},
volume={176},
number={5},
pages={428},
note={},
month={January},
year={1991}}

@article{yevick,
author={M. Glasner and D. Yevick and B. Hermansson },
title={},
journal={Math. and Comp. Mod.},
volume={16},
number={10},
pages={177},
note={},
month={October},
year={1992}}

@article{neuffer,
author={D. Neuffer and E. Forest},
title={{A General Formalism for Quasi-local Correction of Multipole
Distortions in Periodic Transport Systems}},
journal={Phys. Lett. A.},
volume={135},
number={3},
pages={197},
note={},
month={February},
year={1989}}

@techreport{ritson,
author={D. Ritson},
title={{SSCTRK: A Particle tracking Code for the SSC}},
institution={Stanford Linear Accelerator Center},
number={SLAC-PUB-5302 and SSCL-305},
month={July},
year={1990},
note={
Work performed at the now defunct SSC laboratory.}}

@article{leewhiting,
author={G. E. Lee-Whiting},
title={},
journal={Nucl. Instr. Meth.},
volume={83},
number={},
pages={232},
note={},
month={},
year={1970}}

@article{laskar,
author={H. S. Dumas and J. Laskar},
title={{Global Dynamics and Long-Time Stability in Hamiltonian Systems via Numerical Frequency Analysis}},
journal={Phys. Rev. Lett.},
volume={70},
number={20},
pages={2975},
note={},
month={May},
year={1993}}

@techreport{forest138,
author={E. Forest},
title={{Canonical integrators as tracking codes (or How to integrate perturbation theory with tracking)}},
institution={SSC-CDG },
number={SSC-138},
month={},
year={1987},
note={Also part of lectures delivered at Fermi National Laboratory.
}}

@techreport{slac77,
author={K. L. Brown and D. C. Carey and Ch. Iselin and F. Rothacker},
title={{TRANSPORT: a Computer Program for Designing Charged Particle Beam Transport Systems}},
institution={CERN},
number={CERN 80-04},
month={March},
year={1980},
note={
}}

@techreport{slac75,
author={K. L. Brown},
title={{A First and Second Order Matrix Theory for the Design of Beam Transport Systems and Charged Particle Spectrometers}},
institution={SLAC},
number={SLAC Report 75},
month={June},
year={1982},
note={
}}

@article{sanz,
author={J. M. Sanz-Serna},
title={{Global Dynamics and Long-Time Stability in Hamiltonian Systems via Numerical Frequency Analysis}},
journal={Phys. Rev. Lett.},
volume={70},
number={20},
pages={2975},
note={},
month={May},
year={1993}}

@inproceedings{gluck,
booktitle={{Proceedings of the  Linear Accelerator Conference}} ,
title={},
author={R. L. Gluckstern},
publisher={LANL},
address={Los Alamos},
note={},
editor={},
pages={250},
year={1966}}

@misc{racetrack,
note={RACETRACK: A kick code developed by A. Wrulich which uses the matrix-kick split on the small angle
Hamiltonian.}}

@techreport{sixtrack,
author={F. Schmidt},
title={{SIXTRACK}, version 1.2, single particle tracking code treating transverse motion with synchrotron
 oscillations in a symplectic manner},
number={CERN SL/94--56 (AP)},
month={},
year={1994},
institution={CERN}
}

@techreport{sixtracko,
author={G. Ripken},
title={},
institution={DESY},
number={85--084},
month={},
year={1984},
note={This is the oldest reference on SIXTRACK
}}

@book{lakoff,
author={G. Lakoff and M. Johnson },
title={{ Metaphors we live by}} ,
publisher={ University of Chicago Press},
series={},
address={Chicago},
year={1980}}

@book{perko,
author={L. Perko},
title={{ Differential Equations and Dynamical Systems}} ,
publisher={Springer-Verlag},
series={},
address={New York},
year={1991}}

@book{smale,
author={M. W. Hirsch and S. Smale},
title={{ Differential equations, dynamical systems, and linear algebra}} ,
publisher={Academic Press},
series={},
address={New York},
year={1974}}


@techreport{sands,
author={M. Sands},
title={},
institution={Stanford Linear Accelerator},
number={SLAC-121},
month={},
year={1970},
note={
}}

@misc{thor,
note={THOR is an unpublished attempt (but apparently successful) by J. Bengtsson  at producing
a polymorphic environment and a class structure compatible with the requirements of this book
using the C++ language.
}}

@misc{irwin,
author={J. Irwin},
title={},
number={},
month={},
year={},
note={Invited talk at the 1994 Charged Particle Optics conference held in Tsukuba, Japan.
}}

@misc{lielib,
note={LIELIB is a post-processor of the original DA-Package of Berz for the analysis of nonlinear maps
and quadratic moments. It is an integral component of the ``ideal code'' described in this book.}
}

@techreport{oidelec,
author={K. Oide},
title={{Bimu Rikigaku Numon}},
institution={National Laboratory For High Energy Physics (KEK)},
number={KEK Proc. 93-6},
month={June},
year={1993},
note={in Japanese
}}

@techreport{dragtmaxwell,
author={A. J. Dragt et al.},
title={{Numerical Third-Order
Transfer Map for Combined Function Dipole}},
institution={University of Maryland Physics
Department},
number={},
month={},
year={1990},
note={
}}

@inproceedings{willekedonut,
booktitle={{Proceedings  of the Linear Accelerator Conference}} ,
title={{Methods of Beam Optics}},
author={F. Willeke and G. Ripken},
publisher={American Institute of Physics},
address={New York},
note={},
volume={184},
editor={AIP},
pages={758},
year={1989}}

@article{antoniou,
author={I. Antoniou and S. Tasaki},
title={{Spectral Decomposition of the Renyi Map}},
journal={J. Phys. Math. Gen.},
volume={26},
number={},
pages={73},
note={},
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